Potential Method for 3D Wave Propagation in a Poroelastic Medium and Its Applications to Lamb's Problem for a Poroelastic Half-Space

摘要

In cylindrical coordinates, a potential method is developed for three-dimensional (3D) wave propagation in a poroelastic medium. By using the proposed potential method, the wave propagation problems can be reduced to the determination of four scalar potentials governed by four scalar Helmholtz equations, representing the motions of P1, P2, SV, SH waves in the porous media, respectively. By the methods of separation of variables, the general solutions to those Helmholtz equations are found in cylindrical coordinates. Boundary value problems associated with a homogeneous poroelastic half-space loaded by surface tractions, that is, Lamb's problem for a fluid-saturated medium is resolved using the obtained general solutions. It is shown that these potentials introduced in this research for 3D wave propagation problems can also be reduced to those reported by previous researchers for axisymmetric wave propagation in the fluid-saturated porous medium. Furthermore, numerical examples for the state-state and transient responses of the poroelastic half-space are provided.